Will Inpatient psychiatric program care effect my career?

No, it absolutely will not. The army has taken large steps over the last decade or two to encourage soldiers to seek out Mental Health treatments when it's needed.
What will affect your career is if you fail to seek help and it effects your job performance.

My advice, self admit. That is better than being admitted by a doctor. If you self admit, you can choose if you want to later leave. If you are on hold, you are in the system.

As Long As You Make Progress During Therapy, And Come Out with A clean Bill Of Health You Should Be Fine...

Look at it this way - if you did not get some intensive help at this time, maybe the effects on your long term career would be much worse. You have to take care of yourself as best as you can with whatever resources you have. If there are any consequences, like some people might have doubts about your capabilities, you have to avoid telling too much to people who do not need to know, and facing what we all do, that some people are afraid to give someone a chance. If you ever have a superior who ever thinks there is just one way to do things, or just one kind of person who he/she needs, try to get a transfer. You can't reform a poor manager by yourself. Communicate well with your superiors if they are open. Do your best and ask for what you need to succeed if you can think of a way someone can support you. it took a long time for me to be very successful, but i did.

I tell people that our brains, are regulated by chemicals . Does anyone think a diabetic taking a pill to regulate insulin is a big problem? Why is treatment and medication to regulate mental activity a big problem? Just make sure you you have a good Doctor and a good program.